Details

analyze520.0ms (10%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
6.2%	93.6%	0.2%	8
25%	74.9%	0.2%	9
28.1%	71.7%	0.2%	10
29.6%	70.2%	0.2%	11
53%	46.8%	0.2%	12
71.3%	28.5%	0.2%	13
71.7%	28.1%	0.2%	14

Compiler

Compiled 16 to 12 computations (25% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

11.0ms	256×	body	128	valid
1.0ms	18×	body	128	invalid

Compiler

Compiled 31 to 27 computations (12.9% saved)

simplify288.0ms (5.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (123.0ms)

Iter	Nodes	Cost
0	5232	30

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 27.4b

Counts

2 → 1

Compiler

Compiled 30 to 22 computations (26.7% saved)

localize13.0ms (0.3%)

Local error

Found 2 expressions with local error:

1.0b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
26.9b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_2165` `add-cube-cbrt_binary64_2178` `*-un-lft-identity_binary64_2143`
9×	`times-frac_binary64_2149`
4×	`add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`associate-/r_binary64_2087` `associate-/l_binary64_2088`
2×	`pow1_binary64_2204` `flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `div-inv_binary64_2140` `flip3-+_binary64_2146` `cancel-sign-sub-inv_binary64_2109` `flip-+_binary64_2117` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

2 → 44

Calls

2 calls:

10.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series280.0ms (5.4%)

Counts

2 → 6

Calls

2 calls:

197.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
83.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

simplify81.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	6255	1595

prune303.0ms (5.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	41	9	50
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	9	51

Merged error: 26.6b

Counts

51 → 9

Compiler

Compiled 5963 to 3672 computations (38.4% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
18.2b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
27.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.3b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`*-un-lft-identity_binary64_2143`
28×	`sqrt-prod_binary64_2159`
25×	`add-sqr-sqrt_binary64_2165`
24×	`times-frac_binary64_2149`
23×	`add-cube-cbrt_binary64_2178`
10×	`unpow-prod-down_binary64_2222` `distribute-lft-out_binary64_2094`
8×	`associate-/r*_binary64_2087`
6×	`sqrt-div_binary64_2160` `pow1_binary64_2204` `add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`associate-/l*_binary64_2088` `flip3-+_binary64_2146` `flip-+_binary64_2117`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147` `sqrt-pow1_binary64_2161` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `div-inv_binary64_2140` `cancel-sign-sub-inv_binary64_2109` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 96

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
8.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series411.0ms (7.9%)

Counts

4 → 12

Calls

4 calls:

238.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
82.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
46.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
44.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify91.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5542	3247

prune268.0ms (5.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	106	11	117

Merged error: 23.6b

Counts

117 → 11

Compiler

Compiled 5975 to 3239 computations (45.8% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
18.2b	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
27.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

rewrite49.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_2143`
30×	`sqrt-prod_binary64_2159`
25×	`add-sqr-sqrt_binary64_2165`
24×	`times-frac_binary64_2149`
23×	`add-cube-cbrt_binary64_2178`
12×	`unpow-prod-down_binary64_2222` `distribute-lft-out_binary64_2094`
8×	`associate-/r*_binary64_2087`
6×	`sqrt-div_binary64_2160` `pow1_binary64_2204` `add-log-exp_binary64_2182` `add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
3×	`associate-/l*_binary64_2088` `flip3-+_binary64_2146` `flip-+_binary64_2117`
2×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `flip--_binary64_2118` `associate-/r/_binary64_2089` `flip3--_binary64_2147` `sqrt-pow1_binary64_2161` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `diff-log_binary64_2235` `clear-num_binary64_2142` `sub-neg_binary64_2136` `div-inv_binary64_2140` `cancel-sign-sub-inv_binary64_2109` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 98

Calls

4 calls:

16.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))

series418.0ms (8%)

Counts

4 → 12

Calls

4 calls:

249.0ms	(/.f64 (-.f64 (.f64 x.im y.re) (.f64 x.re y.im)) (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2))))
78.0ms	(-.f64 (.f64 x.im y.re) (.f64 x.re y.im))
46.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
45.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5398	3277

prune233.0ms (4.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	108	2	110
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	109	12	121

Merged error: 23.6b

Counts

121 → 12

Compiler

Compiled 4834 to 3024 computations (37.4% saved)

localize24.0ms (0.5%)

Local error

Found 4 expressions with local error:

9.2b	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
27.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.3b	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
27.3b	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

rewrite56.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`sqrt-prod_binary64_2159`
55×	`*-un-lft-identity_binary64_2143`
34×	`add-sqr-sqrt_binary64_2165`
33×	`times-frac_binary64_2149`
31×	`add-cube-cbrt_binary64_2178`
12×	`unpow-prod-down_binary64_2222` `distribute-lft-out_binary64_2094`
11×	`associate-/r*_binary64_2087`
10×	`sqrt-div_binary64_2160`
7×	`pow1_binary64_2204`
6×	`add-exp-log_binary64_2181` `add-cbrt-cube_binary64_2179`
4×	`add-log-exp_binary64_2182` `flip3-+_binary64_2146` `flip-+_binary64_2117`
3×	`rem-sqrt-square_binary64_2156` `pow1/2_binary64_2223` `associate-/l*_binary64_2088` `sqrt-pow1_binary64_2161`
2×	`associate-/r/_binary64_2089` `associate-/l/_binary64_2090`
1×	`cbrt-undiv_binary64_2177` `clear-num_binary64_2142` `flip--_binary64_2118` `div-inv_binary64_2140` `flip3--_binary64_2147` `div-exp_binary64_2194` `frac-2neg_binary64_2154` `div-sub_binary64_2148`

Counts

4 → 113

Calls

4 calls:

17.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
9.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
4.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))

series523.0ms (10%)

Counts

4 → 12

Calls

4 calls:

389.0ms	(/.f64 (-.f64 (.f64 y.re x.im) (.f64 y.im x.re)) (sqrt.f64 (sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))))
48.0ms	(sqrt.f64 (+.f64 (.f64 y.re y.re) (.f64 y.im y.im)))
45.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))
41.0ms	(sqrt.f64 (+.f64 (pow.f64 y.re 2) (pow.f64 y.im 2)))

simplify97.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5568	4113

prune300.0ms (5.8%)

Pruning

13 alts after pruning (10 fresh and 3 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	124	13	137

Merged error: 23.6b

Counts

137 → 13

Compiler

Compiled 6485 to 3595 computations (44.6% saved)

regimes125.0ms (2.4%)

Compiler: Compiled 1232 to 992 computations (19.5% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	51	48
1	51	48

end0.0ms (0%)

sample921.0ms (17.7%)

Algorithm

1×

intervals

Results

343.0ms	8000×	body	128	valid
22.0ms	474×	body	128	invalid

Compiler

Compiled 347 to 275 computations (20.7% saved)

Details

analyze520.0ms (10%)

sample22.0ms (0.4%)

simplify288.0ms (5.5%)

prune3.0ms (0.1%)

localize13.0ms (0.3%)

rewrite18.0ms (0.3%)

series280.0ms (5.4%)

simplify81.0ms (1.5%)

prune303.0ms (5.8%)

localize17.0ms (0.3%)

rewrite47.0ms (0.9%)

series411.0ms (7.9%)

simplify91.0ms (1.7%)

prune268.0ms (5.2%)

localize15.0ms (0.3%)

rewrite49.0ms (0.9%)

series418.0ms (8%)

simplify86.0ms (1.7%)

prune233.0ms (4.5%)

localize24.0ms (0.5%)

rewrite56.0ms (1.1%)

series523.0ms (10%)

simplify97.0ms (1.9%)

prune300.0ms (5.8%)

regimes125.0ms (2.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample921.0ms (17.7%)

Profiling